WASHINGTON (CNN) -- Testimony resumed Monday in a long-running case involving thousands of children with autism that their parents contend was triggered by an early childhood vaccination.

The parents are seeking compensation because the vaccines contained thimerosal, a mercury-derived compound they say helped bring on regressive autism, in which normally developing children suddenly exhibit learning disorders and behavioral problems, typically between ages 1 and 2.

Two families are serving as test cases in this second of a three-phase review of evidence being examined by a special federal court intended to compensate victims of injuries caused by vaccines. Nearly 5,000 other autism claims are pending in the court.

The theory that vaccines or thimerosal can cause autism is not accepted by many medical experts, including the Institute of Medicine, the U.S. Centers for Disease Control and Prevention, and the American Academy of Pediatrics. Multiple scientific studies also have not proved a link.

"In the six years since the U.S. Court of Federal Claims created this proceeding, petitioners have not moved beyond their hypothesis," Ricciardella said.

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"The debate is over," she concluded, "the credible scientific community has rejected it."

But Powers, speaking with reporters during a midday break, said the government's defense rests largely on research done no later than 2004. "There are at least 35 studies, peer-reviewed and published," that the families hope to showcase through expert testimony, he said.

This phase of the litigation is scheduled to run three weeks. Each phase involves a look at representative cases of children with autism and their medical history to help the special masters determine whether there is a link between their disabilities and thimerosal-containing vaccines that would warrant compensation.